Three rates of convergence or separation via U-statistics in a dependent framework. (arXiv:2106.12796v2 [math.ST] UPDATED)

Web: http://arxiv.org/abs/2106.12796

Despite the ubiquity of U-statistics in modern Probability and Statistics,
their non-asymptotic analysis in a dependent framework may have been
overlooked. In a recent work, a new concentration inequality for U-statistics
of order two for uniformly ergodic Markov chains has been proved. In this
paper, we put this theoretical breakthrough into action by pushing further the
current state of knowledge in three different active fields of research. First,
we establish a new exponential inequality for the estimation of spectra of …

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